Elastic Net = Ridge + Lasso

2026-06-13 · Source: DataMListic · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Intermediate, quick

Summary

Elastic Net regression combines the penalties of Ridge and Lasso regression, using an "alpha" parameter to control the blend. Ridge applies a squared penalty, shrinking all coefficients, while Lasso uses an absolute value penalty that can drive coefficients to zero. Geometrically, Ridge constrains coefficients to a circle, Lasso to a diamond, and Elastic Net creates a rounded diamond. This blended approach offers two key benefits: sparsity, inherited from Lasso's sharp corners allowing coefficients to snap to zero, and grouping, derived from Ridge's curved edges, which enables correlated features to shrink together for enhanced stability. Adjusting "alpha" shifts the constraint from a circle (alpha near zero) to a diamond (alpha near one).

Key takeaway

For data scientists building predictive models with highly correlated features, Elastic Net regression offers a superior alternative to standalone Ridge or Lasso. You can achieve both feature sparsity and stable coefficient estimates by tuning the "alpha" parameter, preventing arbitrary feature exclusion common with Lasso. Consider Elastic Net when your dataset includes many interdependent predictors, ensuring a more robust and interpretable model.

Key insights

Elastic Net blends Ridge and Lasso penalties to achieve both sparsity and stable grouping of correlated features.

Principles

• Lasso provides sparsity by driving coefficients to zero.
• Ridge offers stability by shrinking correlated features together.
• Elastic Net's "alpha" controls the blend of penalties.

In practice

• Use Elastic Net for feature selection with correlated predictors.
• Adjust "alpha" to balance sparsity and grouping effects.

Topics

• Elastic Net Regression
• Ridge Regression
• Lasso Regression
• Regularization
• Feature Selection
• Predictive Modeling

Best for: Data Scientist, Machine Learning Engineer, AI Student

Related on AIssential

• Elastic Net - Explained — Elastic Net combines L1 and L2 regularization for stable feature selection and grouping of correlated variables.
• Lasso Regression: Why the Solution Lives on a Diamond — Lasso Regression uses vector projections and coefficient constraints to prevent overfitting by shrinking feature coefficients.
• Ridge Regression is a Gaussian Prior — Ridge regression stabilizes OLS by penalizing large coefficients, preventing overfitting from correlated features.
• Adaptive Forward Stepwise: A Method for High Sparsity Regression — Adaptive Forward Stepwise Regression offers sparser models with shrinkage, outperforming LASSO and Forward Stepwise.
• Canonical Regularisation of Wide Feature-Learning Neural Networks — Traditional ridge regularization biases feature-learning networks due to curved parameter-space geometry, necessitating a geodesic-based approach.
• Which Regularizer Should You Actually Use? Lessons from 134,400 Simulations — Regularizer choice for linear models depends on optimization objective and data characteristics like sample size and multicollinearity.

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Editorial summary, takeaway, and curation by AIssential. Original article published by DataMListic.